Numerical Study of Diffusion of Interacting Particles in a Magnetic Fluid Layer

Lavrova, O. A.; Полевиков, В. К.; Tobiska, Lutz

doi:10.5772/36636

Cited by 2 publications

(3 citation statements)

References 23 publications

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“…The algebraic relation (2.14) was used in [10,11] for computations of the Rosensweig instability in ferrofluids. The form of the magnetization law with concentration changes the relative magnetic permeability of the ferrofluid µ (2) (h) in (2.3) and µ (3) (h) in (2.4) as follows:…”

Section: Mathematical Modelmentioning

confidence: 99%

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Numerical Study of the Shielding Properties of a Ferrofluid Taking Into Account Magnitophoresis and Particle Interaction

Lavrova

Полевиков

2022

Mathematical Modelling and Analysis

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Shielding properties of a cylindrical thick-walled ferrofluid layer that protects against externally applied uniform magnetic fields are numerically investigated. We take into account the diffusion of magnetic nanoparticles in the ferrofluid with magnetic dipole-dipole, steric and hydrodynamic interactions between particles. Permeability of the ferrofluid is considered to be dependent on the magnetic-field strength and the particle concentration. A combined method of finite differences and boundary elements is applied to solve a nonlinear transmission problem of magnetostatics in the whole space, augmented by nonlinear algebraic equations based on the mass transfer equation for magnetic nanoparticles in ferrofluids. Numerical experiments revealed that the diffusion of particles has negligible influence on the shielding properties at weak and strong intensities of the applied magnetic field when comparing with the results of computations for a uniform particle distribution.

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Section: Mathematical Modelmentioning

confidence: 99%

“…Note that the expression for the unknown constant c k+1 is incorrectly written in [10] and should be modified as…”

Section: ∂Cmentioning

confidence: 99%

Numerical Study of the Shielding Properties of a Ferrofluid Taking Into Account Magnitophoresis and Particle Interaction

Lavrova

Полевиков

2022

Mathematical Modelling and Analysis

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“…layer under magnetic force, surface tension force, gravity and hydrodynamics [33,34,35,36]. In [37], the Rosensweig instability is investigated numerically for the diffusion of magnetic particles. The magnetic particle concentration and the free surface shape are part of the solution.…”

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confidence: 99%

Ferrofluids and magnetically guided superparamagnetic particles in flows: a review of simulations and modeling

Afkhami

Renardy

2017

J Eng Math

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Ferrofluids are typically suspensions of magnetite nanoparticles, and behave as a homogeneous continuum. The production of nanoparticles with a narrow size distribution and the achievement of colloidal stability are important technological issues. The ability of the ferrofluid to respond to an external magnetic field in a controllable manner has made it emerge as a smart material in a variety of applications, such as seals, lubricants, electronics cooling, shock absorbers and adaptive optics. Magnetic nanoparticle suspensions have also gained attraction recently in a range of biomedical applications, such as cell separation, hyperthermia, MRI, drug targeting and cancer diagnosis. In this review, we provide an introduction to mathematical modeling of three problems: motion of superparamagnetic nanoparticles in magnetic drug targeting, the motion of a ferrofluid drop consisting of chemically bound nanoparticles without a carrier fluid, and the breakage of a thin film of a ferrofluid.

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Numerical Study of Diffusion of Interacting Particles in a Magnetic Fluid Layer

Cited by 2 publications

References 23 publications

Numerical Study of the Shielding Properties of a Ferrofluid Taking Into Account Magnitophoresis and Particle Interaction

Numerical Study of the Shielding Properties of a Ferrofluid Taking Into Account Magnitophoresis and Particle Interaction

Ferrofluids and magnetically guided superparamagnetic particles in flows: a review of simulations and modeling

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